``Configure'' Parameter Definitions for pythag

1. If the number is still red, you need to hit Enter for the program to know the new number!
2. If the parameters change while the Configure window is open, the window will not reflect the new numbers unless you hit the ``Revert'' button in the top middle. This mostly happens when one loads presets.

• Pulse, Packet, or Wave Shape
  • Amplitude: Maximum y-value of incoming wave/pulse/packet. Initial default 0.05 m = 5 cm.
  • Omega: Angular frequency, in radians per second, for the incoming wave/packet. Ignored for pulses. Initial default 200 rad/sec. Higher frequencies may lead to packets with slightly shifted velocities (dispersion), and eventually (above 1000) to weird effects: change the Numerical Accuracy Controls for high frequencies.
  • FWHM: Width of the packet/pulse in seconds. The ``pulses'' are Gaussians of full width half maximum in time FWHM,
    (amplitude) exp( - 2.7725887 (t-x/v)^2 / FWHM^2 )
    and the ``packets'' are these Gaussians times sine waves. The pulses are lagged by 2*FWHM as they come into the string, so the actual forcing is
    (amplitude) exp( - 2.7725887 (t-2*FWHM)^2 / FWHM^2 )
    Pulses much shorter than 0.01 sec will distort due to dispersion because of lack of spatial resolution (# sites below). Initial default 0.03 sec.
• Mass Density Distribution mu(x)
  • Mu1: The mass per unit length of the first (often the only) segment of string, in kg/m. Initial default 0.1 kg/m.
  • Step X12: The position along the string where the first segment of string ends and the second begins, in meters. Initial default is 10 m, the length of the string (i.e., no second segment).
  • Mu2: The mass per unit length of the second segment of string. Default 0.025 kg/m.
  • Step X23: The position where the second segment ends and the third begins. Initial default is 10 m (no third segment).
  • Mu2: The mass per unit length of the third segment of string. Initial default 0.1 kg/m.
• Graphics Controls
  • X for vs T: Tells where along the string to put the black rectangle. More precisely, this is the point X where Y(X,T) is plotted in the lower left graph by default. Initial default is 5 m (halfway along the string length L).
  • graph time skip: The simulation runs too slowly on even modern workstations if each time-step is displayed. Making this number larger will make the ``vs. X'' display faster: smaller will make the motion smoother. Initial default 20: minimum value 1 (display all time steps).
  • Y mult: The program decides for itself what the vertical range of the graphs should be. You can adjust this by changing this parameter: make it larger to zoom out, make it smaller to make the default range smaller (although it's usually better to zoom and leave the defaults alone). We use this when looking at resonances, for example.
• String State
  • Tension Tau: Tension on the string, in Newtons. Initial default 160 N.
  • Length L: The length of the string, in meters. Initial default 10 m.
• Numerical Accuracy Controls
  • # sites: The number of discrete segments into which the string is decomposed for numerical work. Increase for more accuracy, especially for high frequencies and short pulses. Initial default 257; maximum 999.
  • epsilon_t: The time step by which the simulation is incremented. The leapfrog algorithm used by this simulation is pretty accurate until it goes crazy, so we live on the edge. Doubling it from the default will typically cause the simulation to go unstable. Note: epsilon_t is rescaled whenever tau, muX, nsites, or L are changed. Automatically computed.

Statistical Mechanics: Entropy, Order Parameters, and Complexity, now available at Oxford University Press (USA, Europe).